Two kinds of phase transition in photonic systems with application to optical isolation
Date of Issue2018
School of Physical and Mathematical Sciences
This thesis concerns the study of two kinds of phase transitions, parity-time(P T ) symmetric phase transitions and topological phase transitions, using photonic sys- tems. In the first part of the thesis, we perform a theoretical study of the nonlinear dynamics of a nonlinear optical isolator device based on coupled microcavities with gain and loss. This reveals a correspondence between the boundary of asymptotic stability in the nonlinear regime, where gain saturation is present, and the P T - breaking transition in the underlying linear system. We establish a correspondence between the onset of optical isolation and the P T phase transition of the linear system. In the second part of the thesis, we study a new class of nonlinear optical isolator based on self-induced topological phase transitions. We show that topological phase transitions can be used to help design nonlinear photonic structures exhibiting power thresholds and discontinuities in their transmittance. This provides a novel route to devising nonlinear optical isolators. We study three representative designs: (i) a waveguide array implementing a nonlinear 1D Su-Schrieffer-Heeger model, (ii) a waveguide array implementing a nonlinear 2D Haldane model, and (iii) a 2D lattice of coupled-ring waveguides. In the first two cases, we find a correspondence between the topological transition of the underlying linear lattice and the power threshold of the transmittance, and show that the transmission behavior is attributable to the emergence of a self-induced topological soliton. In the third case, we show that the topological transition produces a discontinuity in the transmittance curve, which can be exploited to achieve sharp jumps in the power-dependent isolation ratio. In the third part, we study the realization of an unpaired Dirac cone at the center of the first Brillouin zone, using a gyromagnetic photonic crystal with broken square sub-lattice symmetry and broken time reversal symmetry. The behavior of the Dirac modes can be described by a gyromagnetic effective medium model with near-zero refractive index. When two domains are subjected to opposite magnetic biases, there exist unidirectional edge states along the domain wall. This establishes a novel link between topological edge states and the surface waves of homogenous magneto-optical media.